TABLE OF CONTENTS Let us consider the linear system sketched in Figure 6.2. Assuming perfect knowledge of the channel matrix H at both transmit and receive sides, in this chapter we will show how to derive the optimal coding matrices F and G, under different optimality criteria and operative constraints. To leave the formulation and solution as general as possible, we do not impose any structure on H, so that the solution can be equally well applied to SISO or MIMO systems. In the ensuing sections, we will specialize the solutions to different transmit/receive structures and propagation characteristics in order to gain physical insight into the optimal strategies.
Denoting by ? the estimated vector, the I/O relationship is
| (6.15) |  |
where s and ? are column vectors of size M, F is N M, H is P N, G is M P and, finally, the noise vector ? has size P 1. To make our formulation as general as possible, to be able to use it for both SISO and MIMO systems, we do not impose any restriction on the sizes of the matrices involved in (6.15). It is important to introduce the mean square error (MSE) matrix, defined as
| (6.16) |  |
Using (6.15), and denoting with R ss and R ?? the covariance matrices of the vectors s and
